I was given a beautiful heavy stainless steel kettle as a wedding present (a very long time ago). It still works fine despite being forgotten, and then boiling until it's dry, and then sitting empty on a high flame about a million times. It's dark, dull, tarnished condition probably displaying more graphically than anything else my tendency to get distracted until I notice "...that burning smell"
I tried steel wool with a gritty cleanser and elbow grease, I tried Wright's silver polish, I even tried my magic trick that works wonders for instantly polishing tarnished silver - soaking in very hot water, salt and a sheet of aluminum foil. Nothing worked.
Surely some domestic chowhound has a great trick for polishing up stainless steel.